Cognitive Turbulence: A Gauge Enstrophy Theory of Thought, Attachment, and Psychosis

We present a mathematical theory of cognitive dynamics based on the gauge enstrophy cascade framework. The theory unifies the physics of turbulent flows with the neurobiology of thought, attachment, and psychotic disorders. We prove arigorous isomorphism between the Amari neural field equation—with a physically justified assumption of non-uniform effective conductivity—and the two-dimensional Navier–Stokes equations with linear Rayleigh friction. In the inertial range, theseequations reduce to the 2D Euler equations, supporting the inverse Kraichnan cas-cade that concentrates neural activity into coherent vortex structures—the attachment vortices that link sensory perception to limbic emotion.We prove that the dynamical properties of an attachment vortex—its resistance to contradiction, self-reinforcement, and concentration of energy—are independent of whether the triggering signal originates externally (love, bonding) or internally(hallucination, delusion). This universality theorem provides the mathematical foundation for understanding psychosis as a misdirected attachment mechanism.The theory synthesises six major hypotheses of schizophrenia—dopaminergic, glutamatergic, thalamic filter, neuroanatomical, self-organised criticality, and connectome-based—into a single enstrophy balance equation with neurotransmitter-modulated parameters. We calibrate these parameters against published PET occupancy datafor five common antipsychotics, transforming the theory from a qualitative framework into a quantitative clinical tool. We derive a prognostic formula for thepoint of no return—the critical accumulated deformation of the connectome beyond which remission is impossible—expressed in terms of clinically measurable quantities: episode duration, symptom severity, and number of prior episodes.We present a three-layer numerical simulation framework implementing the sensory–limbic–plasticity architecture of the theory, with four experimental scenarios: healthy attachment, spontaneous hallucination, antipsychotic intervention, and cumulative deformation. The theory makes quantitative predictions testable with current EEG, fMRI, and clinical data. If confirmed, it would transform psychiatry from an empirical discipline into a branch of applied mathematics—the cognitivehydrodynamics of the human mind.